LMFDB - Embedded newform 576.2.y.a.335.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.9
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433336 + 1.67697i) q^{3} +(-0.923380 - 0.247419i) q^{5} +(1.93471 - 3.35102i) q^{7} +(-2.62444 - 1.45338i) q^{9} +O(q^{10})$	\(q+(-0.433336 + 1.67697i) q^{3} +(-0.923380 - 0.247419i) q^{5} +(1.93471 - 3.35102i) q^{7} +(-2.62444 - 1.45338i) q^{9} +(-3.49688 + 0.936987i) q^{11} +(-6.43770 - 1.72498i) q^{13} +(0.815048 - 1.44126i) q^{15} +3.74282i q^{17} +(-3.09199 - 3.09199i) q^{19} +(4.78118 + 4.69657i) q^{21} +(-0.327240 + 0.188932i) q^{23} +(-3.53871 - 2.04308i) q^{25} +(3.57454 - 3.77130i) q^{27} +(4.14191 - 1.10982i) q^{29} +(0.788179 - 0.455055i) q^{31} +(-0.0559708 - 6.27019i) q^{33} +(-2.61558 + 2.61558i) q^{35} +(-2.13502 - 2.13502i) q^{37} +(5.68242 - 10.0483i) q^{39} +(-3.66866 - 6.35430i) q^{41} +(0.662918 + 2.47404i) q^{43} +(2.06376 + 1.99136i) q^{45} +(-0.0726386 + 0.125814i) q^{47} +(-3.98624 - 6.90437i) q^{49} +(-6.27659 - 1.62190i) q^{51} +(5.67083 - 5.67083i) q^{53} +3.46078 q^{55} +(6.52503 - 3.84529i) q^{57} +(-1.07059 + 3.99549i) q^{59} +(1.69731 + 6.33446i) q^{61} +(-9.94786 + 5.98268i) q^{63} +(5.51765 + 3.18562i) q^{65} +(0.357964 - 1.33594i) q^{67} +(-0.175028 - 0.630643i) q^{69} +9.88796i q^{71} +6.65482i q^{73} +(4.95962 - 5.04897i) q^{75} +(-3.62561 + 13.5309i) q^{77} +(-2.18459 - 1.26127i) q^{79} +(4.77537 + 7.62862i) q^{81} +(0.0699481 + 0.261050i) q^{83} +(0.926045 - 3.45605i) q^{85} +(0.0662949 + 7.42677i) q^{87} -5.86860 q^{89} +(-18.2356 + 18.2356i) q^{91} +(0.421566 + 1.51894i) q^{93} +(2.09006 + 3.62010i) q^{95} +(5.07233 - 8.78553i) q^{97} +(10.5392 + 2.62324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.433336	+	1.67697i	−0.250187	+	0.968198i
$3$	−0.433336	+	1.67697i	−0.250187	+	0.968198i
$4$		0			0
$5$	−0.923380	−	0.247419i	−0.412948	−	0.110649i	0.0463628	−	0.998925i	$-0.485237\pi$
$5$	−0.923380	−	0.247419i	−0.412948	−	0.110649i	−0.459311	+	0.888276i	$0.651904\pi$
$6$		0			0
$7$	1.93471	−	3.35102i	0.731253	−	1.26657i	−0.225094	−	0.974337i	$-0.572269\pi$
$7$	1.93471	−	3.35102i	0.731253	−	1.26657i	0.956348	−	0.292231i	$-0.0943976\pi$
$8$		0			0
$9$	−2.62444	−	1.45338i	−0.874813	−	0.484460i
$10$		0			0
$11$	−3.49688	+	0.936987i	−1.05435	+	0.282512i	−0.744048	−	0.668126i	$-0.767097\pi$
$11$	−3.49688	+	0.936987i	−1.05435	+	0.282512i	−0.310302	+	0.950638i	$0.600430\pi$
$12$		0			0
$13$	−6.43770	−	1.72498i	−1.78550	−	0.478423i	−0.793929	−	0.608010i	$-0.791968\pi$
$13$	−6.43770	−	1.72498i	−1.78550	−	0.478423i	−0.991568	+	0.129587i	$0.958635\pi$
$14$		0			0
$15$	0.815048	−	1.44126i	0.210444	−	0.372132i
$16$		0			0
$17$			3.74282i			0.907767i	0.891061	+	0.453884i	$0.149962\pi$
$17$			3.74282i			0.907767i	−0.891061	+	0.453884i	$0.850038\pi$
$18$		0			0
$19$	−3.09199	−	3.09199i	−0.709351	−	0.709351i	0.257048	−	0.966399i	$-0.417250\pi$
$19$	−3.09199	−	3.09199i	−0.709351	−	0.709351i	−0.966399	+	0.257048i	$0.917250\pi$
$20$		0			0
$21$	4.78118	+	4.69657i	1.04334	+	1.02488i
$22$		0			0
$23$	−0.327240	+	0.188932i	−0.0682344	+	0.0393951i	−0.533729	−	0.845656i	$-0.679210\pi$
$23$	−0.327240	+	0.188932i	−0.0682344	+	0.0393951i	0.465495	+	0.885051i	$0.345876\pi$
$24$		0			0
$25$	−3.53871	−	2.04308i	−0.707742	−	0.408615i
$26$		0			0
$27$	3.57454	−	3.77130i	0.687920	−	0.725786i
$28$		0			0
$29$	4.14191	−	1.10982i	0.769133	−	0.206088i	0.147144	−	0.989115i	$-0.452992\pi$
$29$	4.14191	−	1.10982i	0.769133	−	0.206088i	0.621988	+	0.783027i	$0.286325\pi$
$30$		0			0
$31$	0.788179	−	0.455055i	0.141561	−	0.0817303i	−0.427547	−	0.903993i	$-0.640622\pi$
$31$	0.788179	−	0.455055i	0.141561	−	0.0817303i	0.569108	+	0.822263i	$0.307289\pi$
$32$		0			0
$33$	−0.0559708	−	6.27019i	−0.00974326	−	1.09150i
$34$		0			0
$35$	−2.61558	+	2.61558i	−0.442114	+	0.442114i
$36$		0			0
$37$	−2.13502	−	2.13502i	−0.350996	−	0.350996i	0.509484	−	0.860480i	$-0.329836\pi$
$37$	−2.13502	−	2.13502i	−0.350996	−	0.350996i	−0.860480	+	0.509484i	$0.829836\pi$
$38$		0			0
$39$	5.68242	−	10.0483i	0.909915	−	1.60902i
$40$		0			0
$41$	−3.66866	−	6.35430i	−0.572948	−	0.992375i	−0.996261	−	0.0863918i	$-0.972466\pi$
$41$	−3.66866	−	6.35430i	−0.572948	−	0.992375i	0.423313	−	0.905983i	$-0.360867\pi$
$42$		0			0
$43$	0.662918	+	2.47404i	0.101094	+	0.377288i	0.997873	−	0.0651910i	$-0.0207657\pi$
$43$	0.662918	+	2.47404i	0.101094	+	0.377288i	−0.896779	+	0.442479i	$0.854099\pi$
$44$		0			0
$45$	2.06376	+	1.99136i	0.307647	+	0.296854i
$46$		0			0
$47$	−0.0726386	+	0.125814i	−0.0105954	+	0.0183518i	−0.871275	−	0.490796i	$-0.836706\pi$
$47$	−0.0726386	+	0.125814i	−0.0105954	+	0.0183518i	0.860679	+	0.509148i	$0.170039\pi$
$48$		0			0
$49$	−3.98624	−	6.90437i	−0.569463	−	0.986339i
$50$		0			0
$51$	−6.27659	−	1.62190i	−0.878898	−	0.227111i
$52$		0			0
$53$	5.67083	−	5.67083i	0.778948	−	0.778948i	−0.200704	−	0.979652i	$-0.564323\pi$
$53$	5.67083	−	5.67083i	0.778948	−	0.778948i	0.979652	+	0.200704i	$0.0643229\pi$
$54$		0			0
$55$	3.46078			0.466652
$56$		0			0
$57$	6.52503	−	3.84529i	0.864262	−	0.509322i
$58$		0			0
$59$	−1.07059	+	3.99549i	−0.139379	+	0.520169i	0.860563	+	0.509345i	$0.170112\pi$
$59$	−1.07059	+	3.99549i	−0.139379	+	0.520169i	−0.999941	+	0.0108242i	$0.996554\pi$
$60$		0			0
$61$	1.69731	+	6.33446i	0.217319	+	0.811044i	0.985337	+	0.170617i	$0.0545761\pi$
$61$	1.69731	+	6.33446i	0.217319	+	0.811044i	−0.768019	+	0.640427i	$0.778757\pi$
$62$		0			0
$63$	−9.94786	+	5.98268i	−1.25331	+	0.753747i
$64$		0			0
$65$	5.51765	+	3.18562i	0.684381	+	0.395127i
$66$		0			0
$67$	0.357964	−	1.33594i	0.0437322	−	0.163211i	−0.940606	−	0.339499i	$-0.889742\pi$
$67$	0.357964	−	1.33594i	0.0437322	−	0.163211i	0.984339	+	0.176288i	$0.0564091\pi$
$68$		0			0
$69$	−0.175028	−	0.630643i	−0.0210709	−	0.0759205i
$70$		0			0
$71$			9.88796i			1.17348i	0.809774	+	0.586742i	$0.199590\pi$
$71$			9.88796i			1.17348i	−0.809774	+	0.586742i	$0.800410\pi$
$72$		0			0
$73$			6.65482i			0.778888i	0.921050	+	0.389444i	$0.127333\pi$
$73$			6.65482i			0.778888i	−0.921050	+	0.389444i	$0.872667\pi$
$74$		0			0
$75$	4.95962	−	5.04897i	0.572688	−	0.583004i
$76$		0			0
$77$	−3.62561	+	13.5309i	−0.413176	+	1.54199i
$78$		0			0
$79$	−2.18459	−	1.26127i	−0.245786	−	0.141904i	0.372047	−	0.928214i	$-0.378656\pi$
$79$	−2.18459	−	1.26127i	−0.245786	−	0.141904i	−0.617833	+	0.786309i	$0.711989\pi$
$80$		0			0
$81$	4.77537	+	7.62862i	0.530596	+	0.847625i
$82$		0			0
$83$	0.0699481	+	0.261050i	0.00767780	+	0.0286539i	0.969658	−	0.244464i	$-0.0786119\pi$
$83$	0.0699481	+	0.261050i	0.00767780	+	0.0286539i	−0.961981	+	0.273118i	$0.911945\pi$
$84$		0			0
$85$	0.926045	−	3.45605i	0.100444	−	0.374861i
$86$		0			0
$87$	0.0662949	+	7.42677i	0.00710756	+	0.796233i
$88$		0			0
$89$	−5.86860			−0.622070			−0.311035	−	0.950398i	$-0.600676\pi$
$89$	−5.86860			−0.622070			−0.311035	+	0.950398i	$0.600676\pi$
$90$		0			0
$91$	−18.2356	+	18.2356i	−1.91161	+	1.91161i
$92$		0			0
$93$	0.421566	+	1.51894i	0.0437144	+	0.157507i
$94$		0			0
$95$	2.09006	+	3.62010i	0.214436	+	0.371414i
$96$		0			0
$97$	5.07233	−	8.78553i	0.515017	−	0.892035i	−0.484831	−	0.874608i	$-0.661119\pi$
$97$	5.07233	−	8.78553i	0.515017	−	0.892035i	0.999848	−	0.0174277i	$-0.00554769\pi$
$98$		0			0
$99$	10.5392	+	2.62324i	1.05923	+	0.263646i
$100$		0			0
$101$	0.194443	+	0.725673i	0.0193479	+	0.0722072i	0.974925	−	0.222535i	$-0.0714330\pi$
$101$	0.194443	+	0.725673i	0.0193479	+	0.0722072i	−0.955577	+	0.294742i	$0.904766\pi$
$102$		0			0
$103$	−6.93904	−	12.0188i	−0.683724	−	1.18424i	−0.973836	−	0.227252i	$-0.927026\pi$
$103$	−6.93904	−	12.0188i	−0.683724	−	1.18424i	0.290112	−	0.956993i	$-0.406307\pi$
$104$		0			0
$105$	−3.25282	−	5.51968i	−0.317443	−	0.538665i
$106$		0			0
$107$	−1.56287	−	1.56287i	−0.151088	−	0.151088i	0.627516	−	0.778604i	$-0.284072\pi$
$107$	−1.56287	−	1.56287i	−0.151088	−	0.151088i	−0.778604	+	0.627516i	$0.784072\pi$
$108$		0			0
$109$	6.71432	−	6.71432i	0.643115	−	0.643115i	−0.308205	−	0.951320i	$-0.599728\pi$
$109$	6.71432	−	6.71432i	0.643115	−	0.643115i	0.951320	+	0.308205i	$0.0997283\pi$
$110$		0			0
$111$	4.50555	−	2.65518i	0.427648	−	0.252019i
$112$		0			0
$113$	−13.7148	+	7.91823i	−1.29018	+	0.744885i	−0.978686	−	0.205364i	$-0.934162\pi$
$113$	−13.7148	+	7.91823i	−1.29018	+	0.744885i	−0.311492	+	0.950249i	$0.600829\pi$
$114$		0			0
$115$	0.348913	−	0.0934909i	0.0325363	−	0.00871807i
$116$		0			0
$117$	14.3883	+	13.8835i	1.33020	+	1.28353i
$118$		0			0
$119$	12.5423	+	7.24129i	1.14975	+	0.663808i
$120$		0			0
$121$	1.82398	−	1.05307i	0.165816	−	0.0957339i
$122$		0			0
$123$	12.2457	−	3.39867i	1.10416	−	0.306448i
$124$		0			0
$125$	6.14189	+	6.14189i	0.549347	+	0.549347i
$126$		0			0
$127$		−	10.4492i		−	0.927219i	−0.886040	−	0.463609i	$-0.846554\pi$
$127$		−	10.4492i		−	0.927219i	0.886040	−	0.463609i	$-0.153446\pi$
$128$		0			0
$129$	−4.43616	+	0.0395993i	−0.390582	+	0.00348652i
$130$		0			0
$131$	−18.2908	−	4.90101i	−1.59807	−	0.428203i	−0.653614	−	0.756828i	$-0.726748\pi$
$131$	−18.2908	−	4.90101i	−1.59807	−	0.428203i	−0.944461	+	0.328625i	$0.893415\pi$
$132$		0			0
$133$	−16.3434	+	4.37921i	−1.41716	+	0.379726i
$134$		0			0
$135$	−4.23375	+	2.59793i	−0.364383	+	0.223594i
$136$		0			0
$137$	−7.93788	+	13.7488i	−0.678178	+	1.17464i	0.297350	+	0.954768i	$0.403897\pi$
$137$	−7.93788	+	13.7488i	−0.678178	+	1.17464i	−0.975529	+	0.219871i	$0.929436\pi$
$138$		0			0
$139$	16.4382	+	4.40461i	1.39427	+	0.373594i	0.876285	−	0.481794i	$-0.160015\pi$
$139$	16.4382	+	4.40461i	1.39427	+	0.373594i	0.517988	+	0.855388i	$0.326681\pi$
$140$		0			0
$141$	−0.179509	−	0.176332i	−0.0151174	−	0.0148499i
$142$		0			0
$143$	24.1282			2.01770
$144$		0			0
$145$	−4.09914			−0.340415
$146$		0			0
$147$	13.3058	−	3.69288i	1.09744	−	0.304584i
$148$		0			0
$149$	−6.54234	−	1.75301i	−0.535969	−	0.143613i	−0.0193260	−	0.999813i	$-0.506152\pi$
$149$	−6.54234	−	1.75301i	−0.535969	−	0.143613i	−0.516643	+	0.856201i	$0.672819\pi$
$150$		0			0
$151$	4.39506	−	7.61246i	0.357665	−	0.619493i	−0.629906	−	0.776672i	$-0.716906\pi$
$151$	4.39506	−	7.61246i	0.357665	−	0.619493i	0.987570	+	0.157178i	$0.0502398\pi$
$152$		0			0
$153$	5.43975	−	9.82281i	0.439777	−	0.794127i
$154$		0			0
$155$	−0.840378	+	0.225179i	−0.0675008	+	0.0180868i
$156$		0			0
$157$	−7.30654	−	1.95778i	−0.583126	−	0.156248i	−0.0448162	−	0.998995i	$-0.514270\pi$
$157$	−7.30654	−	1.95778i	−0.583126	−	0.156248i	−0.538310	+	0.842747i	$0.680937\pi$
$158$		0			0
$159$	7.05242	+	11.9672i	0.559293	+	0.949058i
$160$		0			0
$161$			1.46212i			0.115231i
$162$		0			0
$163$	3.88439	+	3.88439i	0.304249	+	0.304249i	0.842674	−	0.538425i	$-0.180980\pi$
$163$	3.88439	+	3.88439i	0.304249	+	0.304249i	−0.538425	+	0.842674i	$0.680980\pi$
$164$		0			0
$165$	−1.49968	+	5.80362i	−0.116750	+	0.451811i
$166$		0			0
$167$	−16.2578	+	9.38644i	−1.25807	+	0.726345i	−0.972698	−	0.232074i	$-0.925449\pi$
$167$	−16.2578	+	9.38644i	−1.25807	+	0.726345i	−0.285367	+	0.958418i	$0.592116\pi$
$168$		0			0
$169$	27.2101	+	15.7098i	2.09309	+	1.20844i
$170$		0			0
$171$	3.62090	+	12.6086i	0.276897	+	0.964202i
$172$		0			0
$173$	−4.46886	+	1.19743i	−0.339761	+	0.0910387i	−0.424665	−	0.905350i	$-0.639608\pi$
$173$	−4.46886	+	1.19743i	−0.339761	+	0.0910387i	0.0849043	+	0.996389i	$0.472942\pi$
$174$		0			0
$175$	−13.6928	+	7.90554i	−1.03508	+	0.597603i
$176$		0			0
$177$	−6.23639	−	3.52674i	−0.468756	−	0.265086i
$178$		0			0
$179$	16.7079	−	16.7079i	1.24881	−	1.24881i	0.292557	−	0.956248i	$-0.405494\pi$
$179$	16.7079	−	16.7079i	1.24881	−	1.24881i	0.956248	−	0.292557i	$-0.0945062\pi$
$180$		0			0
$181$	−3.87025	−	3.87025i	−0.287673	−	0.287673i	0.548486	−	0.836160i	$-0.315204\pi$
$181$	−3.87025	−	3.87025i	−0.287673	−	0.287673i	−0.836160	+	0.548486i	$0.815204\pi$
$182$		0			0
$183$	−11.3582	+	0.101389i	−0.839621	+	0.00749486i
$184$		0			0
$185$	1.44319	+	2.49968i	0.106106	+	0.183780i
$186$		0			0
$187$	−3.50698	−	13.0882i	−0.256455	−	0.957105i
$188$		0			0
$189$	−5.72200	−	19.2747i	−0.416214	−	1.40203i
$190$		0			0
$191$	2.49854	−	4.32759i	0.180788	−	0.313134i	−0.761361	−	0.648328i	$-0.775469\pi$
$191$	2.49854	−	4.32759i	0.180788	−	0.313134i	0.942149	+	0.335194i	$0.108802\pi$
$192$		0			0
$193$	8.77894	+	15.2056i	0.631922	+	1.09452i	0.987158	+	0.159744i	$0.0510670\pi$
$193$	8.77894	+	15.2056i	0.631922	+	1.09452i	−0.355237	+	0.934776i	$0.615600\pi$
$194$		0			0
$195$	−7.73318	+	7.87248i	−0.553784	+	0.563760i
$196$		0			0
$197$	14.4859	−	14.4859i	1.03208	−	1.03208i	0.0326073	−	0.999468i	$-0.489619\pi$
$197$	14.4859	−	14.4859i	1.03208	−	1.03208i	0.999468	−	0.0326073i	$-0.0103811\pi$
$198$		0			0
$199$	0.627801			0.0445037			0.0222518	−	0.999752i	$-0.492916\pi$
$199$	0.627801			0.0445037			0.0222518	+	0.999752i	$0.492916\pi$
$200$		0			0
$201$	2.08521	+	1.17920i	0.147079	+	0.0831746i
$202$		0			0
$203$	4.29437	−	16.0268i	0.301406	−	1.12486i
$204$		0			0
$205$	1.81539	+	6.77513i	0.126792	+	0.473196i
$206$		0			0
$207$	1.13341	−	0.0202364i	0.0787777	−	0.00140653i
$208$		0			0
$209$	13.7095	+	7.91517i	0.948305	+	0.547504i
$210$		0			0
$211$	1.02256	−	3.81624i	0.0703959	−	0.262721i	−0.921754	−	0.387775i	$-0.873244\pi$
$211$	1.02256	−	3.81624i	0.0703959	−	0.262721i	0.992150	+	0.125054i	$0.0399104\pi$
$212$		0			0
$213$	−16.5818	−	4.28481i	−1.13616	−	0.293590i
$214$		0			0
$215$		−	2.44850i		−	0.166986i
$216$		0			0
$217$		−	3.52161i		−	0.239062i
$218$		0			0
$219$	−11.1599	−	2.88377i	−0.754117	−	0.194867i
$220$		0			0
$221$	6.45628	−	24.0952i	0.434296	−	1.62082i
$222$		0			0
$223$	−1.71289	−	0.988940i	−0.114704	−	0.0662243i	0.441550	−	0.897236i	$-0.354429\pi$
$223$	−1.71289	−	0.988940i	−0.114704	−	0.0662243i	−0.556254	+	0.831012i	$0.687762\pi$
$224$		0			0
$225$	6.31777	+	10.5050i	0.421184	+	0.700335i
$226$		0			0
$227$	7.69603	+	28.7220i	0.510803	+	1.90634i	0.411848	+	0.911252i	$0.364883\pi$
$227$	7.69603	+	28.7220i	0.510803	+	1.90634i	0.0989551	+	0.995092i	$0.468450\pi$
$228$		0			0
$229$	3.81849	−	14.2508i	0.252333	−	0.941720i	−0.717222	−	0.696845i	$-0.754586\pi$
$229$	3.81849	−	14.2508i	0.252333	−	0.941720i	0.969555	−	0.244875i	$-0.0787469\pi$
$230$		0			0
$231$	−21.1199	−	11.9435i	−1.38958	−	0.785823i
$232$		0			0
$233$	11.5384			0.755904			0.377952	−	0.925825i	$-0.376628\pi$
$233$	11.5384			0.755904			0.377952	+	0.925825i	$0.376628\pi$
$234$		0			0
$235$	0.0982018	−	0.0982018i	0.00640598	−	0.00640598i
$236$		0			0
$237$	3.06178	−	3.11693i	0.198884	−	0.202466i
$238$		0			0
$239$	−8.60624	−	14.9065i	−0.556692	−	0.964218i	−0.997770	−	0.0667495i	$-0.978737\pi$
$239$	−8.60624	−	14.9065i	−0.556692	−	0.964218i	0.441078	−	0.897469i	$-0.354596\pi$
$240$		0			0
$241$	4.64695	−	8.04875i	0.299336	−	0.518466i	−0.676648	−	0.736307i	$-0.736568\pi$
$241$	4.64695	−	8.04875i	0.299336	−	0.518466i	0.975984	+	0.217841i	$0.0699014\pi$
$242$		0			0
$243$	−14.8623	+	4.70237i	−0.953416	+	0.301657i
$244$		0			0
$245$	1.97254	+	7.36163i	0.126021	+	0.470317i
$246$		0			0
$247$	14.5717	+	25.2389i	0.927175	+	1.60591i
$248$		0			0
$249$	−0.468083	+	0.00417833i	−0.0296636	+	0.000264791i
$250$		0			0
$251$	−20.7722	−	20.7722i	−1.31113	−	1.31113i	−0.920584	−	0.390545i	$-0.872286\pi$
$251$	−20.7722	−	20.7722i	−1.31113	−	1.31113i	−0.390545	−	0.920584i	$-0.627714\pi$
$252$		0			0
$253$	0.967295	−	0.967295i	0.0608133	−	0.0608133i
$254$		0			0
$255$	5.39439	+	3.05058i	0.337810	+	0.191035i
$256$		0			0
$257$	−1.51801	+	0.876421i	−0.0946906	+	0.0546697i	−0.546598	−	0.837395i	$-0.684077\pi$
$257$	−1.51801	+	0.876421i	−0.0946906	+	0.0546697i	0.451907	+	0.892065i	$0.350744\pi$
$258$		0			0
$259$	−11.2852	+	3.02385i	−0.701227	+	0.187893i
$260$		0			0
$261$	−12.4832	−	3.10711i	−0.772689	−	0.192325i
$262$		0			0
$263$	−0.172109	−	0.0993674i	−0.0106127	−	0.00612726i	0.494684	−	0.869073i	$-0.335284\pi$
$263$	−0.172109	−	0.0993674i	−0.0106127	−	0.00612726i	−0.505297	+	0.862946i	$0.668617\pi$
$264$		0			0
$265$	−6.63940	+	3.83326i	−0.407855	+	0.235475i
$266$		0			0
$267$	2.54307	−	9.84144i	0.155634	−	0.602287i
$268$		0			0
$269$	−16.7454	−	16.7454i	−1.02098	−	1.02098i	−0.999775	−	0.0212085i	$-0.993249\pi$
$269$	−16.7454	−	16.7454i	−1.02098	−	1.02098i	−0.0212085	−	0.999775i	$-0.506751\pi$
$270$		0			0
$271$		−	16.8714i		−	1.02487i	−0.858727	−	0.512433i	$-0.828744\pi$
$271$		−	16.8714i		−	1.02487i	0.858727	−	0.512433i	$-0.171256\pi$
$272$		0			0
$273$	−22.6783	−	38.4826i	−1.37255	−	2.32907i
$274$		0			0
$275$	14.2888	+	3.82867i	0.861647	+	0.230878i
$276$		0			0
$277$	−28.2987	+	7.58262i	−1.70031	+	0.455595i	−0.973016	−	0.230736i	$-0.925887\pi$
$277$	−28.2987	+	7.58262i	−1.70031	+	0.455595i	−0.727289	+	0.686331i	$0.759220\pi$
$278$		0			0
$279$	−2.72990	+	0.0487406i	−0.163435	+	0.00291802i
$280$		0			0
$281$	−3.41297	+	5.91144i	−0.203601	+	0.352647i	−0.949686	−	0.313203i	$-0.898598\pi$
$281$	−3.41297	+	5.91144i	−0.203601	+	0.352647i	0.746085	+	0.665851i	$0.231931\pi$
$282$		0			0
$283$	−9.49738	−	2.54482i	−0.564561	−	0.151274i	−0.0347600	−	0.999396i	$-0.511067\pi$
$283$	−9.49738	−	2.54482i	−0.564561	−	0.151274i	−0.529801	+	0.848122i	$0.677733\pi$
$284$		0			0
$285$	−6.97649	+	1.93625i	−0.413251	+	0.114694i
$286$		0			0
$287$	−28.3912			−1.67588
$288$		0			0
$289$	2.99129			0.175959
$290$		0			0
$291$	12.5350	+	12.3132i	0.734816	+	0.721814i
$292$		0			0
$293$	1.85716	+	0.497626i	0.108497	+	0.0290716i	0.312659	−	0.949865i	$-0.398780\pi$
$293$	1.85716	+	0.497626i	0.108497	+	0.0290716i	−0.204162	+	0.978937i	$0.565447\pi$
$294$		0			0
$295$	1.97712	−	3.42448i	0.115112	−	0.199381i
$296$		0			0
$297$	−8.96609	+	16.5371i	−0.520265	+	0.959579i
$298$		0			0
$299$	2.43258	−	0.651808i	0.140680	−	0.0376950i
$300$		0			0
$301$	9.57314	+	2.56512i	0.551787	+	0.147851i
$302$		0			0
$303$	−1.30119	+	0.0116150i	−0.0747514	+	0.000667267i
$304$		0			0
$305$		−	6.26906i		−	0.358965i
$306$		0			0
$307$	9.86559	+	9.86559i	0.563059	+	0.563059i	0.930175	−	0.367116i	$-0.119655\pi$
$307$	9.86559	+	9.86559i	0.563059	+	0.563059i	−0.367116	+	0.930175i	$0.619655\pi$
$308$		0			0
$309$	23.1620	−	6.42838i	1.31764	−	0.365698i
$310$		0			0
$311$	−3.17139	+	1.83100i	−0.179833	+	0.103827i	−0.587214	−	0.809432i	$-0.699775\pi$
$311$	−3.17139	+	1.83100i	−0.179833	+	0.103827i	0.407381	+	0.913258i	$0.366442\pi$
$312$		0			0
$313$	1.08050	+	0.623827i	0.0610735	+	0.0352608i	0.530226	−	0.847856i	$-0.322107\pi$
$313$	1.08050	+	0.623827i	0.0610735	+	0.0352608i	−0.469152	+	0.883117i	$0.655440\pi$
$314$		0			0
$315$	10.6659	−	3.06300i	0.600954	−	0.172581i
$316$		0			0
$317$	−1.52263	+	0.407988i	−0.0855195	+	0.0229149i	−0.301325	−	0.953521i	$-0.597429\pi$
$317$	−1.52263	+	0.407988i	−0.0855195	+	0.0229149i	0.215806	+	0.976436i	$0.430762\pi$
$318$		0			0
$319$	−13.4439	+	7.76183i	−0.752713	+	0.434579i
$320$		0			0
$321$	3.29812	−	1.94363i	0.184083	−	0.108483i
$322$		0			0
$323$	11.5728	−	11.5728i	0.643925	−	0.643925i
$324$		0			0
$325$	19.2569	+	19.2569i	1.06818	+	1.06818i
$326$		0			0
$327$	8.35013	+	14.1692i	0.461763	+	0.783561i
$328$		0			0
$329$	0.281070	+	0.486828i	0.0154959	+	0.0268397i
$330$		0			0
$331$	2.44201	+	9.11372i	0.134225	+	0.500935i	1.00000		0.000501334i	$0.000159580\pi$
$331$	2.44201	+	9.11372i	0.134225	+	0.500935i	−0.865775	+	0.500434i	$0.833174\pi$
$332$		0			0
$333$	2.50024	+	8.70624i	0.137012	+	0.477099i
$334$		0			0
$335$	−0.661073	+	1.14501i	−0.0361183	+	0.0625587i
$336$		0			0
$337$	6.84951	+	11.8637i	0.373117	+	0.646257i	0.990043	−	0.140764i	$-0.0449558\pi$
$337$	6.84951	+	11.8637i	0.373117	+	0.646257i	−0.616927	+	0.787021i	$0.711622\pi$
$338$		0			0
$339$	−7.33551	−	26.4305i	−0.398410	−	1.43551i
$340$		0			0
$341$	−2.32979	+	2.32979i	−0.126165	+	0.126165i
$342$		0			0
$343$	−3.76296			−0.203181
$344$		0			0
$345$	0.00558466	+	0.625628i	0.000300668	+	0.0336827i
$346$		0			0
$347$	−1.33399	+	4.97851i	−0.0716122	+	0.267260i	−0.992444	−	0.122700i	$-0.960845\pi$
$347$	−1.33399	+	4.97851i	−0.0716122	+	0.267260i	0.920832	+	0.389960i	$0.127511\pi$
$348$		0			0
$349$	−6.05230	−	22.5875i	−0.323972	−	1.20908i	−0.915341	−	0.402679i	$-0.868079\pi$
$349$	−6.05230	−	22.5875i	−0.323972	−	1.20908i	0.591369	−	0.806401i	$-0.298588\pi$
$350$		0			0
$351$	−29.5172	+	18.1125i	−1.57551	+	0.966773i
$352$		0			0
$353$	−25.4729	−	14.7068i	−1.35578	−	0.782762i	−0.366732	−	0.930327i	$-0.619523\pi$
$353$	−25.4729	−	14.7068i	−1.35578	−	0.782762i	−0.989052	+	0.147564i	$0.952857\pi$
$354$		0			0
$355$	2.44647	−	9.13034i	0.129845	−	0.484588i
$356$		0			0
$357$	−17.5784	+	17.8951i	−0.930349	+	0.947108i
$358$		0			0
$359$		−	21.1351i		−	1.11547i	−0.830020	−	0.557734i	$-0.811671\pi$
$359$		−	21.1351i		−	1.11547i	0.830020	−	0.557734i	$-0.188329\pi$
$360$		0			0
$361$			0.120784i			0.00635708i
$362$		0			0
$363$	0.975575	+	3.51508i	0.0512044	+	0.184494i
$364$		0			0
$365$	1.64653	−	6.14493i	0.0861833	−	0.321640i
$366$		0			0
$367$	19.9277	+	11.5053i	1.04022	+	0.600569i	0.919895	−	0.392166i	$-0.128274\pi$
$367$	19.9277	+	11.5053i	1.04022	+	0.600569i	0.120322	+	0.992735i	$0.461607\pi$
$368$		0			0
$369$	0.392947	+	22.0084i	0.0204560	+	1.14571i
$370$		0			0
$371$	−8.03165	−	29.9745i	−0.416982	−	1.55620i
$372$		0			0
$373$	−2.63297	+	9.82636i	−0.136330	+	0.508790i	0.863659	+	0.504076i	$0.168167\pi$
$373$	−2.63297	+	9.82636i	−0.136330	+	0.508790i	−0.999989	+	0.00471336i	$0.998500\pi$
$374$		0			0
$375$	−12.9612	+	7.63824i	−0.669316	+	0.394437i
$376$		0			0
$377$	−28.5788			−1.47188
$378$		0			0
$379$	15.2258	−	15.2258i	0.782098	−	0.782098i	−0.198086	−	0.980185i	$-0.563473\pi$
$379$	15.2258	−	15.2258i	0.782098	−	0.782098i	0.980185	+	0.198086i	$0.0634727\pi$
$380$		0			0
$381$	17.5230	+	4.52803i	0.897731	+	0.231978i
$382$		0			0
$383$	4.43034	+	7.67358i	0.226380	+	0.392102i	0.956733	−	0.290969i	$-0.0939776\pi$
$383$	4.43034	+	7.67358i	0.226380	+	0.392102i	−0.730353	+	0.683070i	$0.760644\pi$
$384$		0			0
$385$	6.69563	−	11.5972i	0.341241	−	0.591046i
$386$		0			0
$387$	1.85594	−	7.45645i	0.0943428	−	0.379033i
$388$		0			0
$389$	−7.94756	−	29.6607i	−0.402957	−	1.50386i	−0.807792	−	0.589467i	$-0.799338\pi$
$389$	−7.94756	−	29.6607i	−0.402957	−	1.50386i	0.404835	−	0.914390i	$-0.367329\pi$
$390$		0			0
$391$	−0.707140	−	1.22480i	−0.0357616	−	0.0619409i
$392$		0			0
$393$	16.1449	−	28.5493i	0.814402	−	1.44012i
$394$		0			0
$395$	1.70514	+	1.70514i	0.0857951	+	0.0857951i
$396$		0			0
$397$	13.1585	−	13.1585i	0.660408	−	0.660408i	−0.295068	−	0.955476i	$-0.595342\pi$
$397$	13.1585	−	13.1585i	0.660408	−	0.660408i	0.955476	+	0.295068i	$0.0953425\pi$
$398$		0			0
$399$	−0.261591	−	29.3051i	−0.0130959	−	1.46709i
$400$		0			0
$401$	30.5262	−	17.6243i	1.52440	−	0.880115i	0.524822	−	0.851212i	$-0.324132\pi$
$401$	30.5262	−	17.6243i	1.52440	−	0.880115i	0.999582	−	0.0289028i	$-0.00920133\pi$
$402$		0			0
$403$	−5.85902	+	1.56992i	−0.291859	+	0.0782033i
$404$		0			0
$405$	−2.52201	−	8.22563i	−0.125320	−	0.408735i
$406$		0			0
$407$	9.46642	+	5.46544i	0.469233	+	0.270912i
$408$		0			0
$409$	1.13193	−	0.653522i	0.0559705	−	0.0323146i	−0.471754	−	0.881730i	$-0.656379\pi$
$409$	1.13193	−	0.653522i	0.0559705	−	0.0323146i	0.527724	+	0.849416i	$0.323045\pi$
$410$		0			0
$411$	−19.6165	−	19.2694i	−0.967612	−	0.950490i
$412$		0			0
$413$	11.3177	+	11.3177i	0.556908	+	0.556908i
$414$		0			0
$415$		−	0.258355i		−	0.0126821i
$416$		0			0
$417$	−14.5097	+	25.6577i	−0.710541	+	1.25646i
$418$		0			0
$419$	4.73240	+	1.26804i	0.231193	+	0.0619480i	0.372555	−	0.928010i	$-0.378482\pi$
$419$	4.73240	+	1.26804i	0.231193	+	0.0619480i	−0.141362	+	0.989958i	$0.545148\pi$
$420$		0			0
$421$	13.7395	−	3.68148i	0.669621	−	0.179425i	0.0920372	−	0.995756i	$-0.470662\pi$
$421$	13.7395	−	3.68148i	0.669621	−	0.179425i	0.577584	+	0.816331i	$0.303995\pi$
$422$		0			0
$423$	0.373491	−	0.224619i	0.0181598	−	0.0109214i
$424$		0			0
$425$	7.64687	−	13.2448i	0.370928	−	0.642465i
$426$		0			0
$427$	24.5107	+	6.56763i	1.18616	+	0.317830i
$428$		0			0
$429$	−10.4556	+	40.4622i	−0.504802	+	1.95353i
$430$		0			0
$431$	28.6229			1.37871			0.689357	−	0.724422i	$-0.257893\pi$
$431$	28.6229			1.37871			0.689357	+	0.724422i	$0.257893\pi$
$432$		0			0
$433$	−15.4438			−0.742181			−0.371091	−	0.928597i	$-0.621016\pi$
$433$	−15.4438			−0.742181			−0.371091	+	0.928597i	$0.621016\pi$
$434$		0			0
$435$	1.77631	−	6.87413i	0.0851674	−	0.329589i
$436$		0			0
$437$	1.59600	+	0.427647i	0.0763471	+	0.0204571i
$438$		0			0
$439$	−7.33448	+	12.7037i	−0.350056	+	0.606314i	−0.986259	−	0.165207i	$-0.947171\pi$
$439$	−7.33448	+	12.7037i	−0.350056	+	0.606314i	0.636203	+	0.771522i	$0.280504\pi$
$440$		0			0
$441$	0.426963	+	23.9136i	0.0203316	+	1.13874i
$442$		0			0
$443$	−14.6646	+	3.92938i	−0.696738	+	0.186690i	−0.589769	−	0.807572i	$-0.700781\pi$
$443$	−14.6646	+	3.92938i	−0.696738	+	0.186690i	−0.106969	+	0.994262i	$0.534114\pi$
$444$		0			0
$445$	5.41894	+	1.45200i	0.256883	+	0.0688315i
$446$		0			0
$447$	5.77478	−	10.2116i	0.273138	−	0.482994i
$448$		0			0
$449$		−	24.2954i		−	1.14657i	−0.819356	−	0.573285i	$-0.805669\pi$
$449$		−	24.2954i		−	1.14657i	0.819356	−	0.573285i	$-0.194331\pi$
$450$		0			0
$451$	18.7828	+	18.7828i	0.884446	+	0.884446i
$452$		0			0
$453$	10.8613	+	10.6691i	0.510309	+	0.501279i
$454$		0			0
$455$	21.3502	−	12.3265i	1.00091	−	0.577877i
$456$		0			0
$457$	−28.9197	−	16.6968i	−1.35281	−	0.781043i	−0.364164	−	0.931335i	$-0.618645\pi$
$457$	−28.9197	−	16.6968i	−1.35281	−	0.781043i	−0.988642	+	0.150292i	$0.951979\pi$
$458$		0			0
$459$	14.1153	+	13.3789i	0.658845	+	0.624471i
$460$		0			0
$461$	7.19708	−	1.92845i	0.335201	−	0.0898170i	−0.0872924	−	0.996183i	$-0.527821\pi$
$461$	7.19708	−	1.92845i	0.335201	−	0.0898170i	0.422494	+	0.906366i	$0.361155\pi$
$462$		0			0
$463$	25.3264	−	14.6222i	1.17702	−	0.679550i	0.221693	−	0.975116i	$-0.428842\pi$
$463$	25.3264	−	14.6222i	1.17702	−	0.679550i	0.955322	+	0.295566i	$0.0955083\pi$
$464$		0			0
$465$	−0.0134510	−	1.50686i	−0.000623775	−	0.0698792i
$466$		0			0
$467$	−26.1748	+	26.1748i	−1.21123	+	1.21123i	−0.240604	+	0.970623i	$0.577346\pi$
$467$	−26.1748	+	26.1748i	−1.21123	+	1.21123i	−0.970623	+	0.240604i	$0.922654\pi$
$468$		0			0
$469$	−3.78421	−	3.78421i	−0.174738	−	0.174738i
$470$		0			0
$471$	6.44933	−	11.4045i	0.297169	−	0.525490i
$472$		0			0
$473$	−4.63630	−	8.03030i	−0.213177	−	0.369234i
$474$		0			0
$475$	4.62449	+	17.2588i	0.212186	+	0.791889i
$476$		0			0
$477$	−23.1246	+	6.64087i	−1.05880	+	0.304064i
$478$		0			0
$479$	−11.3632	+	19.6817i	−0.519199	+	0.899279i	0.480552	+	0.876966i	$0.340436\pi$
$479$	−11.3632	+	19.6817i	−0.519199	+	0.899279i	−0.999751	+	0.0223127i	$0.992897\pi$
$480$		0			0
$481$	10.0618	+	17.4275i	0.458777	+	0.794626i
$482$		0			0
$483$	−2.45193	−	0.633590i	−0.111567	−	0.0288293i
$484$		0			0
$485$	−6.85739	+	6.85739i	−0.311378	+	0.311378i
$486$		0			0
$487$	1.44462			0.0654620			0.0327310	−	0.999464i	$-0.489580\pi$
$487$	1.44462			0.0654620			0.0327310	+	0.999464i	$0.489580\pi$
$488$		0			0
$489$	−8.19724	+	4.83075i	−0.370692	+	0.218454i
$490$		0			0
$491$	−1.55708	+	5.81109i	−0.0702699	+	0.262251i	−0.992119	−	0.125298i	$-0.960011\pi$
$491$	−1.55708	+	5.81109i	−0.0702699	+	0.262251i	0.921849	+	0.387549i	$0.126678\pi$
$492$		0			0
$493$	4.15386	+	15.5024i	0.187080	+	0.698193i
$494$		0			0
$495$	−9.08261	−	5.02984i	−0.408233	−	0.226074i
$496$		0			0
$497$	33.1348	+	19.1304i	1.48630	+	0.858114i
$498$		0			0
$499$	1.36132	−	5.08052i	0.0609411	−	0.227435i	−0.928738	−	0.370737i	$-0.879105\pi$
$499$	1.36132	−	5.08052i	0.0609411	−	0.227435i	0.989679	+	0.143302i	$0.0457719\pi$
$500$		0			0
$501$	−8.69567	−	31.3313i	−0.388494	−	1.39978i
$502$		0			0
$503$		−	10.8120i		−	0.482085i	−0.970515	−	0.241043i	$-0.922511\pi$
$503$		−	10.8120i		−	0.482085i	0.970515	−	0.241043i	$-0.0774893\pi$
$504$		0			0
$505$		−	0.718181i		−	0.0319586i
$506$		0			0
$507$	−38.1359	+	38.8229i	−1.69368	+	1.72419i
$508$		0			0
$509$	−6.91687	+	25.8141i	−0.306585	+	1.14419i	0.624988	+	0.780635i	$0.285104\pi$
$509$	−6.91687	+	25.8141i	−0.306585	+	1.14419i	−0.931572	+	0.363556i	$0.881563\pi$
$510$		0			0
$511$	22.3005	+	12.8752i	0.986515	+	0.569564i
$512$		0			0
$513$	−22.7132	+	0.608377i	−1.00281	+	0.0268605i
$514$		0			0
$515$	3.43370	+	12.8147i	0.151307	+	0.564685i
$516$		0			0
$517$	0.136123	−	0.508018i	0.00598668	−	0.0223426i
$518$		0			0
$519$	−0.0715280	−	8.01302i	−0.00313973	−	0.351732i
$520$		0			0
$521$	41.1590			1.80321			0.901605	−	0.432560i	$-0.142390\pi$
$521$	41.1590			1.80321			0.901605	+	0.432560i	$0.142390\pi$
$522$		0			0
$523$	−5.58726	+	5.58726i	−0.244314	+	0.244314i	−0.818632	−	0.574318i	$-0.805267\pi$
$523$	−5.58726	+	5.58726i	−0.244314	+	0.244314i	0.574318	+	0.818632i	$0.305267\pi$
$524$		0			0
$525$	−7.32375	−	26.3881i	−0.319635	−	1.15167i
$526$		0			0
$527$	1.70319	+	2.95001i	0.0741921	+	0.128505i
$528$		0			0
$529$	−11.4286	+	19.7949i	−0.496896	+	0.860649i
$530$		0			0
$531$	8.61667	−	8.92996i	0.373932	−	0.387527i
$532$		0			0
$533$	12.6567	+	47.2355i	0.548223	+	2.04599i
$534$		0			0
$535$	1.05644	+	1.82980i	0.0456737	+	0.0791092i
$536$		0			0
$537$	20.7784	+	35.2587i	0.896656	+	1.52152i
$538$		0			0
$539$	20.4087	+	20.4087i	0.879067	+	0.879067i
$540$		0			0
$541$	−17.0189	+	17.0189i	−0.731702	+	0.731702i	−0.970957	−	0.239255i	$-0.923097\pi$
$541$	−17.0189	+	17.0189i	−0.731702	+	0.731702i	0.239255	+	0.970957i	$0.423097\pi$
$542$		0			0
$543$	8.16740	−	4.81316i	0.350497	−	0.206553i
$544$		0			0
$545$	−7.86112	+	4.53862i	−0.336733	+	0.194413i
$546$		0			0
$547$	−25.9705	+	6.95876i	−1.11042	+	0.297535i	−0.767000	−	0.641648i	$-0.778251\pi$
$547$	−25.9705	+	6.95876i	−1.11042	+	0.297535i	−0.343417	+	0.939183i	$0.611584\pi$
$548$		0			0
$549$	4.75189	−	19.0912i	0.202806	−	0.814794i
$550$		0			0
$551$	−16.2383	−	9.37517i	−0.691774	−	0.399396i
$552$		0			0
$553$	−8.45312	+	4.88041i	−0.359463	+	0.207536i
$554$		0			0
$555$	−4.81727	+	1.33698i	−0.204482	+	0.0567518i
$556$		0			0
$557$	−8.91025	−	8.91025i	−0.377539	−	0.377539i	0.492674	−	0.870214i	$-0.336019\pi$
$557$	−8.91025	−	8.91025i	−0.377539	−	0.377539i	−0.870214	+	0.492674i	$0.836019\pi$
$558$		0			0
$559$		−	17.0707i		−	0.722013i
$560$		0			0
$561$	23.4682	−	0.209488i	0.990828	−	0.00884461i
$562$		0			0
$563$	−10.9577	−	2.93610i	−0.461811	−	0.123742i	0.0204094	−	0.999792i	$-0.493503\pi$
$563$	−10.9577	−	2.93610i	−0.461811	−	0.123742i	−0.482221	+	0.876050i	$0.660170\pi$
$564$		0			0
$565$	14.6231	−	3.91824i	0.615197	−	0.164842i
$566$		0			0
$567$	34.8027	−	1.24316i	1.46157	−	0.0522077i
$568$		0			0
$569$	11.0917	−	19.2114i	0.464989	−	0.805384i	−0.534212	−	0.845350i	$-0.679392\pi$
$569$	11.0917	−	19.2114i	0.464989	−	0.805384i	0.999201	+	0.0399662i	$0.0127250\pi$
$570$		0			0
$571$	5.38105	+	1.44185i	0.225190	+	0.0603394i	0.369650	−	0.929171i	$-0.379478\pi$
$571$	5.38105	+	1.44185i	0.225190	+	0.0603394i	−0.144460	+	0.989511i	$0.546144\pi$
$572$		0			0
$573$	6.17452	+	6.06527i	0.257944	+	0.253380i
$574$		0			0
$575$	1.54401			0.0643898
$576$		0			0
$577$	−17.9547			−0.747466			−0.373733	−	0.927536i	$-0.621922\pi$
$577$	−17.9547			−0.747466			−0.373733	+	0.927536i	$0.621922\pi$
$578$		0			0
$579$	−29.3035	+	8.13287i	−1.21781	+	0.337991i
$580$		0			0
$581$	1.01011	+	0.270659i	0.0419066	+	0.0112288i
$582$		0			0
$583$	−14.5167	+	25.1437i	−0.601222	+	1.04135i
$584$		0			0
$585$	−9.85083	−	16.3797i	−0.407282	−	0.677218i
$586$		0			0
$587$	28.0419	−	7.51380i	1.15741	−	0.310128i	0.371480	−	0.928441i	$-0.378850\pi$
$587$	28.0419	−	7.51380i	1.15741	−	0.310128i	0.785932	+	0.618313i	$0.212184\pi$
$588$		0			0
$589$	−3.84407	−	1.03001i	−0.158392	−	0.0424410i
$590$		0			0
$591$	18.0151	+	30.5696i	0.741041	+	1.25746i
$592$		0			0
$593$		−	0.243119i		−	0.00998372i	−0.999988	−	0.00499186i	$-0.998411\pi$
$593$		−	0.243119i		−	0.00998372i	0.999988	−	0.00499186i	$-0.00158896\pi$
$594$		0			0
$595$	−9.78966	−	9.78966i	−0.401337	−	0.401337i
$596$		0			0
$597$	−0.272049	+	1.05280i	−0.0111342	+	0.0430883i
$598$		0			0
$599$	0.307246	−	0.177389i	0.0125537	−	0.00724791i	−0.493710	−	0.869627i	$-0.664360\pi$
$599$	0.307246	−	0.177389i	0.0125537	−	0.00724791i	0.506264	+	0.862379i	$0.331026\pi$
$600$		0			0
$601$	−12.9273	−	7.46358i	−0.527316	−	0.304446i	0.212607	−	0.977138i	$-0.431805\pi$
$601$	−12.9273	−	7.46358i	−0.527316	−	0.304446i	−0.739923	+	0.672692i	$0.765138\pi$
$602$		0			0
$603$	−2.88108	+	2.98583i	−0.117327	+	0.121593i
$604$		0			0
$605$	−1.94477	+	0.521101i	−0.0790663	+	0.0211858i
$606$		0			0
$607$	−35.2640	+	20.3597i	−1.43132	+	0.826375i	−0.997222	−	0.0744894i	$-0.976267\pi$
$607$	−35.2640	+	20.3597i	−1.43132	+	0.826375i	−0.434101	+	0.900864i	$0.642934\pi$
$608$		0			0
$609$	25.0155	+	14.1465i	1.01368	+	0.573246i
$610$		0			0
$611$	0.684652	−	0.684652i	0.0276980	−	0.0276980i
$612$		0			0
$613$	30.0647	+	30.0647i	1.21430	+	1.21430i	0.969597	+	0.244706i	$0.0786913\pi$
$613$	30.0647	+	30.0647i	1.21430	+	1.21430i	0.244706	+	0.969597i	$0.421309\pi$
$614$		0			0
$615$	−12.1483	+	0.108442i	−0.489869	+	0.00437280i
$616$		0			0
$617$	−10.8854	−	18.8541i	−0.438231	−	0.759038i	0.559323	−	0.828950i	$-0.311061\pi$
$617$	−10.8854	−	18.8541i	−0.438231	−	0.759038i	−0.997553	+	0.0699125i	$0.977728\pi$
$618$		0			0
$619$	−10.1255	−	37.7889i	−0.406978	−	1.51886i	−0.800378	−	0.599496i	$-0.795368\pi$
$619$	−10.1255	−	37.7889i	−0.406978	−	1.51886i	0.393399	−	0.919368i	$-0.371299\pi$
$620$		0			0
$621$	−0.457213	+	1.90947i	−0.0183473	+	0.0766243i
$622$		0			0
$623$	−11.3541	+	19.6658i	−0.454891	+	0.787894i
$624$		0			0
$625$	6.06371	+	10.5026i	0.242548	+	0.420106i
$626$		0			0
$627$	−19.2143	+	19.5604i	−0.767345	+	0.781168i
$628$		0			0
$629$	7.99101	−	7.99101i	0.318622	−	0.318622i
$630$		0			0
$631$	39.4346			1.56987			0.784934	−	0.619579i	$-0.212697\pi$
$631$	39.4346			1.56987			0.784934	+	0.619579i	$0.212697\pi$
$632$		0			0
$633$	5.95660	+	3.36852i	0.236754	+	0.133886i
$634$		0			0
$635$	−2.58534	+	9.64861i	−0.102596	+	0.382893i
$636$		0			0
$637$	13.7524	+	51.3245i	0.544888	+	2.03355i
$638$		0			0
$639$	14.3710	−	25.9503i	0.568507	−	1.02658i
$640$		0			0
$641$	−25.2321	−	14.5677i	−0.996606	−	0.575391i	−0.0893639	−	0.995999i	$-0.528483\pi$
$641$	−25.2321	−	14.5677i	−0.996606	−	0.575391i	−0.907242	+	0.420608i	$0.861817\pi$
$642$		0			0
$643$	−0.237903	+	0.887866i	−0.00938197	+	0.0350140i	−0.970458	−	0.241270i	$-0.922436\pi$
$643$	−0.237903	+	0.887866i	−0.00938197	+	0.0350140i	0.961076	+	0.276284i	$0.0891029\pi$
$644$		0			0
$645$	4.10606	+	1.06102i	0.161676	+	0.0417778i
$646$		0			0
$647$		−	36.0035i		−	1.41544i	−0.706491	−	0.707722i	$-0.749723\pi$
$647$		−	36.0035i		−	1.41544i	0.706491	−	0.707722i	$-0.250277\pi$
$648$		0			0
$649$		−	14.9749i		−	0.587817i
$650$		0			0
$651$	5.90562	+	1.52604i	0.231460	+	0.0598102i
$652$		0			0
$653$	0.220799	−	0.824032i	0.00864052	−	0.0322468i	−0.961471	−	0.274906i	$-0.911353\pi$
$653$	0.220799	−	0.824032i	0.00864052	−	0.0322468i	0.970112	+	0.242660i	$0.0780198\pi$
$654$		0			0
$655$	15.6768	+	9.05098i	0.612542	+	0.353651i
$656$		0			0
$657$	9.67199	−	17.4652i	0.377340	−	0.681381i
$658$		0			0
$659$	−2.06253	−	7.69747i	−0.0803448	−	0.299851i	0.914047	−	0.405608i	$-0.132940\pi$
$659$	−2.06253	−	7.69747i	−0.0803448	−	0.299851i	−0.994392	+	0.105757i	$0.966273\pi$
$660$		0			0
$661$	5.68510	−	21.2171i	0.221125	−	0.825249i	−0.762795	−	0.646640i	$-0.776174\pi$
$661$	5.68510	−	21.2171i	0.221125	−	0.825249i	0.983920	−	0.178609i	$-0.0571598\pi$
$662$		0			0
$663$	37.6091	+	21.2683i	1.46062	+	0.825991i
$664$		0			0
$665$	16.1747			0.627228
$666$		0			0
$667$	−1.14572	+	1.14572i	−0.0443624	+	0.0443624i
$668$		0			0
$669$	2.40068	−	2.44392i	0.0928156	−	0.0944876i
$670$		0			0
$671$	−11.8706	−	20.5605i	−0.458260	−	0.793730i
$672$		0			0
$673$	22.9778	−	39.7988i	0.885731	−	1.53413i	0.0408565	−	0.999165i	$-0.486991\pi$
$673$	22.9778	−	39.7988i	0.885731	−	1.53413i	0.844874	−	0.534965i	$-0.179675\pi$
$674$		0			0
$675$	−20.3543	+	6.04248i	−0.783438	+	0.232575i
$676$		0			0
$677$	1.97264	+	7.36199i	0.0758147	+	0.282944i	0.993417	−	0.114556i	$-0.0365445\pi$
$677$	1.97264	+	7.36199i	0.0758147	+	0.282944i	−0.917602	+	0.397500i	$0.869878\pi$
$678$		0			0
$679$	−19.6270	−	33.9950i	−0.753216	−	1.30461i
$680$		0			0
$681$	−51.5008	+	0.459721i	−1.97351	+	0.0176165i
$682$		0			0
$683$	17.1824	+	17.1824i	0.657466	+	0.657466i	0.954780	−	0.297314i	$-0.0960908\pi$
$683$	17.1824	+	17.1824i	0.657466	+	0.657466i	−0.297314	+	0.954780i	$0.596091\pi$
$684$		0			0
$685$	10.7314	−	10.7314i	0.410025	−	0.410025i
$686$		0			0
$687$	22.2435	+	12.5789i	0.848641	+	0.479914i
$688$		0			0
$689$	−46.2891	+	26.7250i	−1.76348	+	1.01814i
$690$		0			0
$691$	7.38572	−	1.97900i	0.280966	−	0.0752846i	−0.115584	−	0.993298i	$-0.536874\pi$
$691$	7.38572	−	1.97900i	0.280966	−	0.0752846i	0.396550	+	0.918013i	$0.370207\pi$
$692$		0			0
$693$	29.1808	−	30.2418i	1.10849	−	1.14879i
$694$		0			0
$695$	−14.0890	−	8.13426i	−0.534424	−	0.308550i
$696$		0			0
$697$	23.7830	−	13.7311i	0.900846	−	0.520104i
$698$		0			0
$699$	−5.00000	+	19.3495i	−0.189117	+	0.731865i
$700$		0			0
$701$	20.1418	+	20.1418i	0.760747	+	0.760747i	0.976457	−	0.215711i	$-0.0692068\pi$
$701$	20.1418	+	20.1418i	0.760747	+	0.760747i	−0.215711	+	0.976457i	$0.569207\pi$
$702$		0			0
$703$			13.2029i			0.497958i
$704$		0			0
$705$	0.122127	+	0.207236i	0.00459956	+	0.00780494i
$706$		0			0
$707$	2.80794	+	0.752385i	0.105603	+	0.0282964i
$708$		0			0
$709$	30.2366	−	8.10188i	1.13556	−	0.304272i	0.358396	−	0.933570i	$-0.383324\pi$
$709$	30.2366	−	8.10188i	1.13556	−	0.304272i	0.777165	+	0.629297i	$0.216657\pi$
$710$		0			0
$711$	3.90021	+	6.48518i	0.146269	+	0.243213i
$712$		0			0
$713$	−0.171949	+	0.297825i	−0.00643955	+	0.0111536i
$714$		0			0
$715$	−22.2795	−	5.96977i	−0.833206	−	0.223257i
$716$		0			0
$717$	28.7270	−	7.97289i	1.07283	−	0.297753i
$718$		0			0
$719$	−45.7985			−1.70800			−0.853999	−	0.520275i	$-0.825829\pi$
$719$	−45.7985			−1.70800			−0.853999	+	0.520275i	$0.825829\pi$
$720$		0			0
$721$	−53.7003			−1.99990
$722$		0			0
$723$	11.4838	+	11.2806i	0.427087	+	0.419530i
$724$		0			0
$725$	−16.9245	−	4.53489i	−0.628559	−	0.168422i
$726$		0			0
$727$	−4.35110	+	7.53632i	−0.161373	+	0.279507i	−0.935361	−	0.353693i	$-0.884926\pi$
$727$	−4.35110	+	7.53632i	−0.161373	+	0.279507i	0.773988	+	0.633200i	$0.218259\pi$
$728$		0			0
$729$	−1.44536	−	26.9613i	−0.0535319	−	0.998566i
$730$		0			0
$731$	−9.25990	+	2.48118i	−0.342490	+	0.0917699i
$732$		0			0
$733$	−25.1847	−	6.74821i	−0.930217	−	0.249251i	−0.238270	−	0.971199i	$-0.576580\pi$
$733$	−25.1847	−	6.74821i	−0.930217	−	0.249251i	−0.691947	+	0.721948i	$0.743247\pi$
$734$		0			0
$735$	−13.2000	+	0.117829i	−0.486889	+	0.00434621i
$736$		0			0
$737$			5.00703i			0.184436i
$738$		0			0
$739$	−4.46836	−	4.46836i	−0.164371	−	0.164371i	0.620129	−	0.784500i	$-0.287080\pi$
$739$	−4.46836	−	4.46836i	−0.164371	−	0.164371i	−0.784500	+	0.620129i	$0.787080\pi$
$740$		0			0
$741$	−48.6393	+	13.4993i	−1.78681	+	0.495910i
$742$		0			0
$743$	6.20834	−	3.58439i	0.227762	−	0.131499i	−0.381777	−	0.924254i	$-0.624688\pi$
$743$	6.20834	−	3.58439i	0.227762	−	0.131499i	0.609539	+	0.792756i	$0.291354\pi$
$744$		0			0
$745$	5.60734	+	3.23740i	0.205437	+	0.118609i
$746$		0			0
$747$	0.195830	−	0.786770i	0.00716506	−	0.0287864i
$748$		0			0
$749$	−8.26090	+	2.21350i	−0.301847	+	0.0808796i
$750$		0			0
$751$	−11.9726	+	6.91239i	−0.436887	+	0.252237i	−0.702276	−	0.711905i	$-0.747833\pi$
$751$	−11.9726	+	6.91239i	−0.436887	+	0.252237i	0.265389	+	0.964141i	$0.414500\pi$
$752$		0			0
$753$	43.8356	−	25.8329i	1.59746	−	0.941405i
$754$		0			0
$755$	−5.94177	+	5.94177i	−0.216243	+	0.216243i
$756$		0			0
$757$	−11.5484	−	11.5484i	−0.419735	−	0.419735i	0.465378	−	0.885112i	$-0.345919\pi$
$757$	−11.5484	−	11.5484i	−0.419735	−	0.419735i	−0.885112	+	0.465378i	$0.845919\pi$
$758$		0			0
$759$	1.20296	+	2.04129i	0.0436646	+	0.0740940i
$760$		0			0
$761$	24.0288	+	41.6190i	0.871042	+	1.50869i	0.860920	+	0.508741i	$0.169889\pi$
$761$	24.0288	+	41.6190i	0.871042	+	1.50869i	0.0101223	+	0.999949i	$0.496778\pi$
$762$		0			0
$763$	−9.50955	−	35.4901i	−0.344269	−	1.28483i
$764$		0			0
$765$	−7.45330	+	7.72429i	−0.269475	+	0.279272i
$766$		0			0
$767$	13.7843	−	23.8751i	0.497721	−	0.862078i
$768$		0			0
$769$	4.47454	+	7.75012i	0.161356	+	0.279477i	0.935355	−	0.353710i	$-0.115080\pi$
$769$	4.47454	+	7.75012i	0.161356	+	0.279477i	−0.773999	+	0.633186i	$0.781747\pi$
$770$		0			0
$771$	−0.811923	−	2.92543i	−0.0292407	−	0.105357i
$772$		0			0
$773$	−26.5172	+	26.5172i	−0.953758	+	0.953758i	−0.998977	−	0.0452194i	$-0.985601\pi$
$773$	−26.5172	+	26.5172i	−0.953758	+	0.953758i	0.0452194	+	0.998977i	$0.485601\pi$
$774$		0			0
$775$	−3.71885			−0.133585
$776$		0			0
$777$	−0.180629	−	20.2352i	−0.00648004	−	0.725934i
$778$		0			0
$779$	−8.30398	+	30.9909i	−0.297521	+	1.11036i
$780$		0			0
$781$	−9.26489	−	34.5770i	−0.331524	−	1.23726i
$782$		0			0
$783$	10.6199	−	19.5874i	0.379526	−	0.699998i
$784$		0			0
$785$	6.26233	+	3.61556i	0.223512	+	0.129045i
$786$		0			0
$787$	7.69420	−	28.7151i	0.274268	−	1.02358i	−0.682062	−	0.731295i	$-0.738916\pi$
$787$	7.69420	−	28.7151i	0.274268	−	1.02358i	0.956330	−	0.292289i	$-0.0944169\pi$
$788$		0			0
$789$	0.241217	−	0.245562i	0.00858756	−	0.00874225i
$790$		0			0
$791$			61.2781i			2.17880i
$792$		0			0
$793$		−	43.7072i		−	1.55209i
$794$		0			0
$795$	−3.55116	−	12.7951i	−0.125947	−	0.453797i
$796$		0			0
$797$	5.53663	−	20.6630i	0.196118	−	0.731921i	−0.795857	−	0.605485i	$-0.792979\pi$
$797$	5.53663	−	20.6630i	0.196118	−	0.731921i	0.991975	−	0.126436i	$-0.0403540\pi$
$798$		0			0
$799$	−0.470898	−	0.271873i	−0.0166592	−	0.00961819i
$800$		0			0
$801$	15.4018	+	8.52931i	0.544195	+	0.301368i
$802$		0			0
$803$	−6.23548	−	23.2711i	−0.220045	−	0.821221i
$804$		0			0
$805$	0.361756	−	1.35009i	0.0127502	−	0.0475845i
$806$		0			0
$807$	35.3378	−	20.8251i	1.24395	−	0.733077i
$808$		0			0
$809$	−26.2708			−0.923632			−0.461816	−	0.886976i	$-0.652802\pi$
$809$	−26.2708			−0.923632			−0.461816	+	0.886976i	$0.652802\pi$
$810$		0			0
$811$	0.268850	−	0.268850i	0.00944059	−	0.00944059i	−0.702371	−	0.711811i	$-0.747875\pi$
$811$	0.268850	−	0.268850i	0.00944059	−	0.00944059i	0.711811	+	0.702371i	$0.247875\pi$
$812$		0			0
$813$	28.2928	+	7.31100i	0.992273	+	0.256408i
$814$		0			0
$815$	−2.62570	−	4.54784i	−0.0919741	−	0.159304i
$816$		0			0
$817$	5.59998	−	9.69945i	0.195919	−	0.339341i
$818$		0			0
$819$	74.3613	−	21.3549i	2.59840	−	0.746201i
$820$		0			0
$821$	1.19461	+	4.45834i	0.0416921	+	0.155597i	0.983634	−	0.180180i	$-0.0576679\pi$
$821$	1.19461	+	4.45834i	0.0416921	+	0.155597i	−0.941942	+	0.335777i	$0.891001\pi$
$822$		0			0
$823$	−26.4439	−	45.8021i	−0.921776	−	1.59656i	−0.796666	−	0.604420i	$-0.793405\pi$
$823$	−26.4439	−	45.8021i	−0.921776	−	1.59656i	−0.125110	−	0.992143i	$-0.539928\pi$
$824$		0			0
$825$	−12.6124	+	22.3028i	−0.439108	+	0.776482i
$826$		0			0
$827$	17.9135	+	17.9135i	0.622914	+	0.622914i	0.946275	−	0.323362i	$-0.104813\pi$
$827$	17.9135	+	17.9135i	0.622914	+	0.622914i	−0.323362	+	0.946275i	$0.604813\pi$
$828$		0			0
$829$	−33.9865	+	33.9865i	−1.18040	+	1.18040i	−0.200759	+	0.979641i	$0.564341\pi$
$829$	−33.9865	+	33.9865i	−1.18040	+	1.18040i	−0.979641	+	0.200759i	$0.935659\pi$
$830$		0			0
$831$	−0.452946	−	50.7419i	−0.0157125	−	1.76022i
$832$		0			0
$833$	25.8418	−	14.9198i	0.895366	−	0.516940i
$834$		0			0
$835$	17.3345	−	4.64477i	0.599885	−	0.160739i
$836$		0			0
$837$	1.10123	−	4.59907i	0.0380640	−	0.158967i
$838$		0			0
$839$	4.43002	+	2.55767i	0.152941	+	0.0883007i	0.574518	−	0.818492i	$-0.305190\pi$
$839$	4.43002	+	2.55767i	0.152941	+	0.0883007i	−0.421576	+	0.906793i	$0.638523\pi$
$840$		0			0
$841$	−9.19106	+	5.30646i	−0.316933	+	0.182981i
$842$		0			0
$843$	−8.43433	−	8.28509i	−0.290494	−	0.285354i
$844$		0			0
$845$	−21.2384	−	21.2384i	−0.730623	−	0.730623i
$846$		0			0
$847$		−	8.14959i		−	0.280023i
$848$		0			0
$849$	8.38313	−	14.8240i	0.287708	−	0.508760i
$850$		0			0
$851$	1.10204	+	0.295291i	0.0377775	+	0.0101224i
$852$		0			0
$853$	−11.8803	+	3.18332i	−0.406774	+	0.108995i	−0.456403	−	0.889773i	$-0.650863\pi$
$853$	−11.8803	+	3.18332i	−0.406774	+	0.108995i	0.0496295	+	0.998768i	$0.484196\pi$
$854$		0			0
$855$	−0.223865	−	12.5384i	−0.00765603	−	0.428804i
$856$		0			0
$857$	−23.2496	+	40.2696i	−0.794193	+	1.37558i	0.129158	+	0.991624i	$0.458773\pi$
$857$	−23.2496	+	40.2696i	−0.794193	+	1.37558i	−0.923351	+	0.383958i	$0.874561\pi$
$858$		0			0
$859$	0.881454	+	0.236185i	0.0300748	+	0.00805852i	0.273825	−	0.961780i	$-0.411711\pi$
$859$	0.881454	+	0.236185i	0.0300748	+	0.00805852i	−0.243750	+	0.969838i	$0.578378\pi$
$860$		0			0
$861$	12.3029	−	47.6112i	0.419283	−	1.62258i
$862$		0			0
$863$	−8.62192			−0.293494			−0.146747	−	0.989174i	$-0.546880\pi$
$863$	−8.62192			−0.293494			−0.146747	+	0.989174i	$0.546880\pi$
$864$		0			0
$865$	4.42272			0.150377
$866$		0			0
$867$	−1.29624	+	5.01630i	−0.0440225	+	0.170363i
$868$		0			0
$869$	8.82106	+	2.36359i	0.299234	+	0.0801795i
$870$		0			0
$871$	−4.60893	+	7.98290i	−0.156168	+	0.270490i
$872$		0			0
$873$	−26.0807	+	15.6851i	−0.882699	+	0.530859i
$874$		0			0
$875$	32.4644	−	8.69881i	1.09750	−	0.294074i
$876$		0			0
$877$	−8.95831	−	2.40037i	−0.302501	−	0.0810548i	0.104376	−	0.994538i	$-0.466715\pi$
$877$	−8.95831	−	2.40037i	−0.302501	−	0.0810548i	−0.406877	+	0.913483i	$0.633382\pi$
$878$		0			0
$879$	−1.63928	+	2.89876i	−0.0552915	+	0.0977729i
$880$		0			0
$881$		−	15.7006i		−	0.528967i	−0.964390	−	0.264483i	$-0.914799\pi$
$881$		−	15.7006i		−	0.528967i	0.964390	−	0.264483i	$-0.0852014\pi$
$882$		0			0
$883$	−19.0929	−	19.0929i	−0.642526	−	0.642526i	0.308650	−	0.951176i	$-0.400123\pi$
$883$	−19.0929	−	19.0929i	−0.642526	−	0.642526i	−0.951176	+	0.308650i	$0.900123\pi$
$884$		0			0
$885$	4.88598	+	4.79952i	0.164240	+	0.161334i
$886$		0			0
$887$	13.7996	−	7.96720i	0.463345	−	0.267513i	−0.250105	−	0.968219i	$-0.580465\pi$
$887$	13.7996	−	7.96720i	0.463345	−	0.267513i	0.713450	+	0.700706i	$0.247132\pi$
$888$		0			0
$889$	−35.0156	−	20.2163i	−1.17439	−	0.678032i
$890$		0			0
$891$	−23.8468	−	22.2020i	−0.798899	−	0.743793i
$892$		0			0
$893$	0.613613	−	0.164417i	0.0205338	−	0.00550201i
$894$		0			0
$895$	−19.5616	+	11.2939i	−0.653871	+	0.377513i
$896$		0			0
$897$	0.0389356	+	4.36181i	0.00130002	+	0.145637i
$898$		0			0
$899$	2.75953	−	2.75953i	0.0920356	−	0.0920356i
$900$		0			0
$901$	21.2249	+	21.2249i	0.707104	+	0.707104i
$902$		0			0
$903$	−8.45000	+	14.9423i	−0.281198	+	0.497248i
$904$		0			0
$905$	2.61614	+	4.53128i	0.0869634	+	0.150625i
$906$		0			0
$907$	−9.35177	−	34.9013i	−0.310520	−	1.15888i	−0.928088	−	0.372360i	$-0.878549\pi$
$907$	−9.35177	−	34.9013i	−0.310520	−	1.15888i	0.617568	−	0.786517i	$-0.288118\pi$
$908$		0			0
$909$	0.544374	−	2.18709i	0.0180558	−	0.0725410i
$910$		0			0
$911$	22.5779	−	39.1061i	0.748040	−	1.29564i	−0.200721	−	0.979648i	$-0.564329\pi$
$911$	22.5779	−	39.1061i	0.748040	−	1.29564i	0.948761	−	0.315994i	$-0.102338\pi$
$912$		0			0
$913$	−0.489201	−	0.847320i	−0.0161902	−	0.0280422i
$914$		0			0
$915$	10.5130	+	2.71661i	0.347549	+	0.0898084i
$916$		0			0
$917$	−51.8109	+	51.8109i	−1.71095	+	1.71095i
$918$		0			0
$919$	−50.2366			−1.65715			−0.828575	−	0.559877i	$-0.810848\pi$
$919$	−50.2366			−1.65715			−0.828575	+	0.559877i	$0.810848\pi$
$920$		0			0
$921$	−20.8194	+	12.2692i	−0.686022	+	0.404282i
$922$		0			0
$923$	17.0565	−	63.6557i	0.561421	−	2.09525i
$924$		0			0
$925$	3.19322	+	11.9172i	0.104992	+	0.391837i
$926$		0			0
$927$	0.743235	+	41.6276i	0.0244111	+	1.36723i
$928$		0			0
$929$	−34.6234	−	19.9898i	−1.13596	−	0.655844i	−0.190530	−	0.981681i	$-0.561021\pi$
$929$	−34.6234	−	19.9898i	−1.13596	−	0.655844i	−0.945426	+	0.325837i	$0.894354\pi$
$930$		0			0
$931$	−9.02283	+	33.6737i	−0.295711	+	1.10361i
$932$		0			0
$933$	−1.69625	−	6.11176i	−0.0555328	−	0.200090i
$934$		0			0
$935$			12.9531i			0.423611i
$936$		0			0
$937$			50.1813i			1.63935i	0.572828	+	0.819675i	$0.305846\pi$
$937$			50.1813i			1.63935i	−0.572828	+	0.819675i	$0.694154\pi$
$938$		0			0
$939$	−1.51436	+	1.54164i	−0.0494192	+	0.0503094i
$940$		0			0
$941$	−10.2601	+	38.2914i	−0.334471	+	1.24826i	0.569970	+	0.821665i	$0.306955\pi$
$941$	−10.2601	+	38.2914i	−0.334471	+	1.24826i	−0.904442	+	0.426598i	$0.859712\pi$
$942$		0			0
$943$	2.40107	+	1.38626i	0.0781895	+	0.0451427i
$944$		0			0
$945$	0.514640	+	19.2136i	0.0167412	+	0.625020i
$946$		0			0
$947$	3.40647	+	12.7131i	0.110695	+	0.413121i	0.998929	−	0.0462714i	$-0.0147339\pi$
$947$	3.40647	+	12.7131i	0.110695	+	0.413121i	−0.888233	+	0.459392i	$0.848067\pi$
$948$		0			0
$949$	11.4794	−	42.8418i	0.372638	−	1.39070i
$950$		0			0
$951$	−0.0243711	−	2.73020i	−0.000790286	−	0.0885327i
$952$		0			0
$953$	−10.3207			−0.334320			−0.167160	−	0.985930i	$-0.553460\pi$
$953$	−10.3207			−0.334320			−0.167160	+	0.985930i	$0.553460\pi$
$954$		0			0
$955$	−3.37783	+	3.37783i	−0.109304	+	0.109304i
$956$		0			0
$957$	−7.19061	−	25.9084i	−0.232439	−	0.837500i
$958$		0			0
$959$	30.7150	+	53.2000i	0.991841	+	1.71792i
$960$		0			0
$961$	−15.0858	+	26.1295i	−0.486640	+	0.842886i
$962$		0			0
$963$	1.83021	+	6.37308i	0.0589776	+	0.205370i
$964$		0			0
$965$	−4.34415	−	16.2126i	−0.139843	−	0.521902i
$966$		0			0
$967$	25.6787	+	44.4768i	0.825771	+	1.43028i	0.901329	+	0.433136i	$0.142593\pi$
$967$	25.6787	+	44.4768i	0.825771	+	1.43028i	−0.0755575	+	0.997141i	$0.524074\pi$
$968$		0			0
$969$	14.3922	+	24.4220i	0.462345	+	0.784549i
$970$		0			0
$971$	14.0572	+	14.0572i	0.451117	+	0.451117i	0.895725	−	0.444608i	$-0.146657\pi$
$971$	14.0572	+	14.0572i	0.451117	+	0.451117i	−0.444608	+	0.895725i	$0.646657\pi$
$972$		0			0
$973$	46.5632	−	46.5632i	1.49275	−	1.49275i
$974$		0			0
$975$	−40.6379	+	23.9485i	−1.30146	+	0.766966i
$976$		0			0
$977$	26.6234	−	15.3711i	0.851759	−	0.491764i	−0.00948463	−	0.999955i	$-0.503019\pi$
$977$	26.6234	−	15.3711i	0.851759	−	0.491764i	0.861244	+	0.508191i	$0.169686\pi$
$978$		0			0
$979$	20.5218	−	5.49880i	0.655880	−	0.175742i
$980$		0			0
$981$	−27.3798	+	7.86285i	−0.874169	+	0.251042i
$982$		0			0
$983$	−36.6682	−	21.1704i	−1.16953	−	0.675230i	−0.215963	−	0.976402i	$-0.569289\pi$
$983$	−36.6682	−	21.1704i	−1.16953	−	0.675230i	−0.953570	+	0.301172i	$0.902622\pi$
$984$		0			0
$985$	−16.9600	+	9.79189i	−0.540392	+	0.311995i
$986$		0			0
$987$	−0.938192	+	0.260385i	−0.0298630	+	0.00828816i
$988$		0			0
$989$	−0.684361	−	0.684361i	−0.0217614	−	0.0217614i
$990$		0			0
$991$			37.3774i			1.18733i	0.804711	+	0.593666i	$0.202320\pi$
$991$			37.3774i			1.18733i	−0.804711	+	0.593666i	$0.797680\pi$
$992$		0			0
$993$	−16.3416	+	0.145873i	−0.518586	+	0.00462915i
$994$		0			0
$995$	−0.579699	−	0.155330i	−0.0183777	−	0.00492429i
$996$		0			0
$997$	−1.61228	+	0.432008i	−0.0510613	+	0.0136818i	−0.284259	−	0.958747i	$-0.591748\pi$
$997$	−1.61228	+	0.432008i	−0.0510613	+	0.0136818i	0.233198	+	0.972429i	$0.425081\pi$
$998$		0			0
$999$	−15.6835	+	0.420085i	−0.496205	+	0.0132909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.9		88
3.2	odd	2		1728.2.z.a.143.14		88
4.3	odd	2		144.2.u.a.11.22	✓	88
9.4	even	3		1728.2.z.a.719.14		88
9.5	odd	6	inner	576.2.y.a.527.21		88
12.11	even	2		432.2.v.a.251.1		88
16.3	odd	4	inner	576.2.y.a.47.21		88
16.13	even	4		144.2.u.a.83.16	yes	88
36.23	even	6		144.2.u.a.59.16	yes	88
36.31	odd	6		432.2.v.a.395.7		88
48.29	odd	4		432.2.v.a.35.7		88
48.35	even	4		1728.2.z.a.1007.14		88
144.13	even	12		432.2.v.a.179.1		88
144.67	odd	12		1728.2.z.a.1583.14		88
144.77	odd	12		144.2.u.a.131.22	yes	88
144.131	even	12	inner	576.2.y.a.239.9		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.22	✓	88	4.3	odd	2
144.2.u.a.59.16	yes	88	36.23	even	6
144.2.u.a.83.16	yes	88	16.13	even	4
144.2.u.a.131.22	yes	88	144.77	odd	12
432.2.v.a.35.7		88	48.29	odd	4
432.2.v.a.179.1		88	144.13	even	12
432.2.v.a.251.1		88	12.11	even	2
432.2.v.a.395.7		88	36.31	odd	6
576.2.y.a.47.21		88	16.3	odd	4	inner
576.2.y.a.239.9		88	144.131	even	12	inner
576.2.y.a.335.9		88	1.1	even	1	trivial
576.2.y.a.527.21		88	9.5	odd	6	inner
1728.2.z.a.143.14		88	3.2	odd	2
1728.2.z.a.719.14		88	9.4	even	3
1728.2.z.a.1007.14		88	48.35	even	4
1728.2.z.a.1583.14		88	144.67	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.433336 + 1.67697i) q^{3} +(-0.923380 - 0.247419i) q^{5} +(1.93471 - 3.35102i) q^{7} +(-2.62444 - 1.45338i) q^{9} +O(q^{10})\)	\(q+(-0.433336 + 1.67697i) q^{3} +(-0.923380 - 0.247419i) q^{5} +(1.93471 - 3.35102i) q^{7} +(-2.62444 - 1.45338i) q^{9} +(-3.49688 + 0.936987i) q^{11} +(-6.43770 - 1.72498i) q^{13} +(0.815048 - 1.44126i) q^{15} +3.74282i q^{17} +(-3.09199 - 3.09199i) q^{19} +(4.78118 + 4.69657i) q^{21} +(-0.327240 + 0.188932i) q^{23} +(-3.53871 - 2.04308i) q^{25} +(3.57454 - 3.77130i) q^{27} +(4.14191 - 1.10982i) q^{29} +(0.788179 - 0.455055i) q^{31} +(-0.0559708 - 6.27019i) q^{33} +(-2.61558 + 2.61558i) q^{35} +(-2.13502 - 2.13502i) q^{37} +(5.68242 - 10.0483i) q^{39} +(-3.66866 - 6.35430i) q^{41} +(0.662918 + 2.47404i) q^{43} +(2.06376 + 1.99136i) q^{45} +(-0.0726386 + 0.125814i) q^{47} +(-3.98624 - 6.90437i) q^{49} +(-6.27659 - 1.62190i) q^{51} +(5.67083 - 5.67083i) q^{53} +3.46078 q^{55} +(6.52503 - 3.84529i) q^{57} +(-1.07059 + 3.99549i) q^{59} +(1.69731 + 6.33446i) q^{61} +(-9.94786 + 5.98268i) q^{63} +(5.51765 + 3.18562i) q^{65} +(0.357964 - 1.33594i) q^{67} +(-0.175028 - 0.630643i) q^{69} +9.88796i q^{71} +6.65482i q^{73} +(4.95962 - 5.04897i) q^{75} +(-3.62561 + 13.5309i) q^{77} +(-2.18459 - 1.26127i) q^{79} +(4.77537 + 7.62862i) q^{81} +(0.0699481 + 0.261050i) q^{83} +(0.926045 - 3.45605i) q^{85} +(0.0662949 + 7.42677i) q^{87} -5.86860 q^{89} +(-18.2356 + 18.2356i) q^{91} +(0.421566 + 1.51894i) q^{93} +(2.09006 + 3.62010i) q^{95} +(5.07233 - 8.78553i) q^{97} +(10.5392 + 2.62324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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